Maclaurin Mathematical Olympiad 2017 Q6

The diagram shows a semicircle of radius $r$ inside a right-angled triangle. The shorter edges of the triangle are tangents to the semicircle, and have lengths $a$ and $b$. The diameter of the semicircle lies on the hypotenuse of the triangle.

Prove that $\frac{1}{r}=\frac{1}{a}+P$ where $P$ is an expression to be found.